
Discrete Mathematics
A Concise Introduction
George Tourlakis(Author)
Springer (Publisher)
Published on 4. January 2024
Book
Hardback
XVIII, 253 pages
978-3-031-30487-3 (ISBN)
Description
This book is ideal for a first or second year discrete mathematics course for mathematics, engineering, and computer science majors. The author has extensively class-tested early conceptions of the book over the years and supplements mathematical arguments with informal discussions to aid readers in understanding the presented topics. "Safe" - that is, paradox-free - informal set theory is introduced following on the heels of Russell's Paradox as well as the topics of finite, countable, and uncountable sets with an exposition and use of Cantor's diagonalisation technique. Predicate logic "for the user" is introduced along with axioms and rules and extensive examples. Partial orders and the
minimal condition
are studied in detail with the latter shown to be equivalent to the
induction principle
. Mathematical induction is illustrated with several examples and is followed by a thorough exposition of inductive definitions of
functions
and
sets
. Techniques for solving recurrence relations including generating functions, the O- and o-notations, and trees are provided. Over 200 end of chapter exercises are included to further aid in the understanding and applications of discrete mathematics.
Reviews / Votes
"The book is recommended . . Each chapter concludes with many exercises . . The student who masters this book will have learned the foundations of discrete mathematics!" (Padraig Ó Catháin, zbMATH 1541.05001, 2024)
More details
Series
Edition
2024 ed.
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Illustrations
22 s/w Abbildungen, 2 farbige Abbildungen
XVIII, 253 p. 24 illus., 2 illus. in color.
Dimensions
Height: 246 mm
Width: 173 mm
Thickness: 21 mm
Weight
638 gr
ISBN-13
978-3-031-30487-3 (9783031304873)
DOI
10.1007/978-3-031-30488-0
Schweitzer Classification
Other editions
Additional editions

Book
01/2025
Springer
€48.14
Shipment within 15-20 days

E-Book
01/2024
Springer
€48.14
Available for download
Person
George Tourlakis
, Ph.D., is a Professor in the Department of Electrical Engineering and Computer Science at York University, Toronto, Canada. He obtained his B.Sc. in mechanical and electrical engineering from the National Technical University of Athens and his M.Sc. and Ph.D. in computer science from the University of Toronto. Dr. Tourlakis has authored eight books in computability, logic, and axiomatic set theory and has also authored several journal articles in computability and modal logic. His research interests include calculational logic, modal logic, proof theory, computability with partial oracles, and complexity theory.
Content
Elementary Informal Set Theory.- Safe Set Theory.- Relations and Functions.- A Tiny Bit of Informal Logic.- Inductively Defined Sets and Structural Induction.- Recurrence Equations.- Trees and Graphs.